The stock market and non financial markets are complex systems in which one or more stocks, goods, services, or their derivatives are sold or bought. Many techniques exist that attempt to analyze expected behavior of these markets, including predictions of price and volatility for a forward time series from any given date. Among these methods are those concerning prediction of volatility based on Black Scholes, and implied volatility given prices of options and the assumptions of Gaussian random walks in prices that are used to back estimate the volatility implied by actual option prices. In addition, procedures exist which posit some mathematical form for a feature such as volatility, such as truncated Levy, or Levy, or other distributions, then attempts to fit observed volatility distributions using these assumed underlying distributions and appropriate weighting of coefficients in the given mathematical form.
Still other attempts to predict expected volatility uses Black Scholes formalism but treats variance in price as itself a random variable which changes over time, then attempts to estimate the rate of change of this random variable. Still other efforts to predict volatility are based on causal models of various kinds. For example, some workers postulate a “herding” effect in which clusters of traders of various sizes form and trade in much the same way, causing small and large fluctuations in price, hence in volatility. Other attempts are based on Langevain equations which represent displacement of buy and sell orders at a moment from “equilibrium”, then seek stochastic equations describing the change of this displacement as a function of drift terms, price momentum terms, penalties for price variance, and volatility growth terms. Still other efforts are based on local linear models which embed a single stock's price series, or sometimes several price series, in a multidimensional space of the past N periods and attempts to locally fit the next price move of one or several prices.
The predictive capability of each of these economic model can vary with the economic environment. Specifically, an economic model may exhibit a good predictive capability for one set of economic circumstances and a poor predictive capability for another set of economic circumstances. Since the economic environment changes with time, the utility of each economic model also changes with time.
A great many researchers in economics, finance, and related areas have investigated different aspects of financial markets or markets in general. Topics of interest to the researchers and of relevance to our project have included diffusion of information in markets (Kyle, Albert S. (1985): “Continuous Auctions and Insider Trading,” Econometrica, v. 57, 1315-35, Grossman, Sanford J., and Joseph E. Stiglitz (1980): “On the Impossibility of Informationally Efficient Markets,” The American Economic Review, v. 70, 393-408), efficiency and statistical modeling of markets (Foley (1982)), speculation and bubble formation (Tirole, Jean (1982): “On the Possibility of Speculation Under Rational Expectations,” Econometrica, v. 50, 1163-81.), and many others.
Other existing work in market microstructure theory (O′Hara Blackwell, Maureen, Market Microstructure Theory, Cambridge, Mass., 1995.) suffers from a lack of means for experimental verification (with some important exceptions, such as (Rust, John, John Miner, and Richard Palmer (1993): “Behavior of Trading Automata in a computerized Double Auction Market”, in The Double Auction Market). For example, Glosten-Milgrom (GM) model examines the relationship between Dealer spreads and the proportion of informed Investors in the market. But it is very difficult to quantify the fundamental concept of “proportion of informed investors in the market” Ideally, one would prefer a numerical and experimental framework in which one could examine the regions of validity of analytic models like the GM.
Another important shortcoming of the existing literature is the static nature of most of the models, i.e., results even for dynamic models are usually derived using some type of equilibrium assumptions. Such assumptions greatly limit one's ability to investigate dynamic, potentially non-equilibrium behavior of the system, and also one's ability to model realistically the market participants and as the result the market itself.
Accordingly, there exists a need for a broad encompassing algorithmic framework to develop effective and routinely improvable models and predictions of economic markets including stock markets and non-securities markets. In addition, there exists a need for a broad and improvable algorithmic framework to seek means to price securities such as options and other derivatives.
There exists a further need for a system for performing analysis and making predictions in a securities market using an agent-based models of the dealers and investors.